Stop using NotificationService in ContentStabilityMetricsProvider.

Bug: 357627,1174762,1174769
Change-Id: I6abbe7c3e0602b67bf127765be747f695303ab62
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3411431


Reviewed-by: Scott Violet <sky@chromium.org>
Reviewed-by: Alexei Svitkine <asvitkine@chromium.org>
Reviewed-by: Bo Liu <boliu@chromium.org>
Commit-Queue: Steve Kobes <skobes@chromium.org>
Cr-Commit-Position: refs/heads/main@{#963059}